The unstable temporal development of axi-symmetric jets of incompressible fluid

TL;DR

This paper investigates the linear and non-linear instability development of axi-symmetric incompressible fluid jets, introducing a novel spectral numerical model that captures the transition from initial disturbances to complex non-linear behaviors.

Contribution

It presents a new spectral Galerkin numerical model for simulating the non-linear evolution of axi-symmetric jets, validated against linear theory and capable of capturing complex non-linear phenomena.

Findings

Model agrees with linear theory for small disturbances

Captures non-linear cylindrical roll-up of jets

Demonstrates viability of spectral method for fluid jet simulations

Abstract

We study the shear-driven instability, of Kelvin-Helmholtz type, that forms at the interface between a cylindrical jet of flowing fluid and its surroundings. The results of an infinitesimal-amplitude theory based on linearising the system about the undisturbed jet are given. A novel numerical model based on the Galerkin spectral method is developed and employed to simulate the non-linear development of the jet in the weakly-compressible Boussinesq regime. Representative results demonstrating the viability of this model are given, and are shown to agree with the linear analysis for small disturbances, but to develop cylindrical roll-up in the severely non-linear regime.